Consider the following normal form stage game. Player 1 is the row player and player 2 is the column player. Both players have two actions A and B:
x,5
2,0
6,1
3,1
In the above normal form game, cell (1,1) represents the action profile (A,A), (1,2) represents (A,B), (2,1) represents (B,A) and (2,2) represents (B,B). Suppose x can
only take integer values.
It is given that the stage game has only two pure strategy Nash equilibria: (B,A) and (B,B). Suppose the game is repeated for two periods. The minimum value of x
such that in this repeated game (A,A) is played in a Subgame Perfect Nash Equilibrium is given by:
3
1
5
2